Redundancy analysis is a constrained ordination method that can be used to determine the extent to which one set of variables (explanatory variables) explains the variation in another set of variables (response variables), i.e. it is the multivariate analog of a simple linear regression (Oksanen et al. 2010). It assumes that the relationship between the dependent (response) and independent (explanatory) variables is linear. Here, it can be applied to understand which environmental parameters of the grow-out pond significantly explain a component of the observed pattern of genetic variation of progeny (Forester et al. 2016, 2018).

A partial RDA enables examining the effect of a set of variables (explanatory variables, X) on a response matrix (Y) while controlling for a set of conditioning variables (Z) and can be applied in a case such as here where the strong effect of a set of well-characterized variables (parentage/family) might obscure the signal of a second set of variables (environmental conditions).

Prepare data sets

Response variables (genotypes)

Thin SNPs so only one SNP per contig is retained to reduce linkage among markers.


# thin SNPs within 350 bp of each other
vcftools --vcf data/GENOME_SCAN/SOC.yoy.genotyped.recode.vcf --out data/GENOME_SCAN/SOC.yoy.thinned --thin 350 --recode --recode-INFO-all

Format response variables (genetic data) as allele counts per locus and individual, homozygous genotypes are coded as 0 or 2, heterozygotes as 1.

RDA requires a complete data set, therefore missing values are replaced with the mean allele frequency.

The response variables consist of 2023 loci genotyped for 828 progeny across three spawning events (three sample points per spawning event).

Conditioning variables: Family

Parentage (dam + sire) of each offspring creates the dominant signal in the data set. Because categorical data cannot be used, parentage will be converted into “dummy variables”, i.e. we will create a matrix with each row corresponding to a single progeny and on column per potential parent. Parents will be coded as 1 non-parental adults as 0.

Explanatory variables: Environmental data of grow-out ponds

The spawning events took place in 2017 (N = 1) and 2018 (N = 2). Grow-out ponds exclude predators and ensure abundant prey and while physical parameters (temperature, dissolved oxygen, pH, and salinity) are monitored, they are not controlled with the exception of dissolved oxygen which is maintained by an active water paddle which can be manipulated.

Table 1: Number of individuals at different stages (incubator, stocking into grow-out ponds, harvest) and comparison of survival in incubator and grow-out pond.

EVENT	EGGS_INCUBATED	FRY_HARVESTED	FRY_STOCKED	YOY_HARVESTED	PROP_SURV_INCUB	PROP_SURV_POND
YOY-1	1050000	625628	395254	111306	0.60	0.28
YOY-2	690000	375560	375560	343508	0.54	0.91
YOY-3	1510000	784554	428230	30099	0.52	0.07

The number of eggs placed in the incubator is largely consistent across spawning events 1 and 3 (approx. 1 Mill). By contrast, for spawning event 2 only approximate 690,000 were placed in the incubator; despite though the number of brood fish involved in the spawning event 2 being the highest (individuals from 4 tanks compared to 2 and 3).

Though fry were stocked into the grow-out ponds at similar levels (375,000 - 428,000) the proprtion of progeny that survived to be harvested for stocking varied greatly from 7% (spawning event 3), to 28% spawning event 1, and 91% (spawning event 2). By contrast, survival during the time in the incubator was largely consistent (52 - 60%).

Despite spawning event 2 having the lowest number of eggs incubated, due to the highest proportion of progeny surviving to the next stage both in the incubator and the grow-out pond it had the highest number of progeny harvested for stocking at 343,000 compared to 111,000 and 30,000 for spawning event 1 and 3, respectively. This could be due to differences in environmental conditions of the pond or due to the fact that this pond was harvested early due to construction.

Fig 1: Change in length [mm] of progreny over time spend in grow-out pond for each spawning event.

## 
##  linear regression growth YOY-1

## 
## Call:
## lm(formula = LENGTH ~ DAY, data = tmp)
## 
## Residuals:
##       1       2       3       4       5 
##  1.0008 -0.4809 -0.8673 -0.4354  0.7828 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  6.55836    1.48335   4.421   0.0215 *
## DAY          0.29545    0.06571   4.496   0.0205 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9639 on 3 degrees of freedom
## Multiple R-squared:  0.8708, Adjusted R-squared:  0.8277 
## F-statistic: 20.22 on 1 and 3 DF,  p-value: 0.02054

## slope (growth) for spawning event 1: 0.3

## 
##  linear regression growth YOY-2

## 
## Call:
## lm(formula = LENGTH ~ DAY, data = tmp)
## 
## Residuals:
##       1       2       3       4       5       6       7 
## -2.9313  0.3588 -0.2878  4.5290  0.4725  1.2160 -3.3573 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  13.2183     3.1577   4.186   0.0086 **
## DAY           0.3366     0.1074   3.135   0.0258 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.908 on 5 degrees of freedom
## Multiple R-squared:  0.6629, Adjusted R-squared:  0.5954 
## F-statistic: 9.831 on 1 and 5 DF,  p-value: 0.0258

## slope (growth) for spawning event 2: 0.34

## 
##  linear regression growth YOY-3

## 
## Call:
## lm(formula = LENGTH ~ DAY, data = tmp)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9572 -0.9204  0.3286  0.9082  1.9897 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.11013    1.21904   5.833 0.000642 ***
## DAY          0.10409    0.03448   3.019 0.019410 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.48 on 7 degrees of freedom
## Multiple R-squared:  0.5656, Adjusted R-squared:  0.5036 
## F-statistic: 9.115 on 1 and 7 DF,  p-value: 0.01941

## slope (growth) for spawning event 3: 0.1

Linear regressions show a similar slope for spawning event 1 and 2 (0.3 and 0.34), while the slope for spawning event three is lower (0.1); indicating slowest growth. Generally, fish are expected to spend approximately 30 days in a pond and be about 3 cm when harvested, though growth rates may differ among ponds, especially due to differences in temperature.

Fish were harvested from grow-out pond 2 at a shorter size (approx 1.5 cm) than usually desired (2.5 - 3 cm) due to construction. Due to slow, growth fish from pond 3 were also harvested at a smaller age and spent the most amount of time in the grow-out ponds (> 50).

Fig 2a: Change of physical parameters (temperature, dissolved oxygen, pH, and salinity) measured in each grow-out pond during culture for spawning event 1. Dashed vertical lines indicate sample points T1, T2, and T3. Dissolved oxygen and temperature are measures three times a day, in the morning (blue), afternoon (red), and evening (green).

Pond culture for spawning event 3 is characterized by a decrease in temperature between sampling point T1 and T2 which then increases again to experience a second more steep (but not as drastic) decline.

Fig 2b: Change of physical parameters (temperature, dissolved oxygen, pH, and salinity) measured in each grow-out pond during culture for spawning event 2. Dashed vertical lines indicate sample points T1, T2, and T3. Dissolved oxygen and temperature are measures three times a day, in the morning (blue), afternoon (red), and evening (green).

Spawning event 2 has comparatively lower salinity overall and experiences a steep decline in temperature after sampling point T2 after which there is a slow, steady increase in temperature.

Fig 2c: Change of physical parameters (temperature, dissolved oxygen, pH, and salinity) measured in each grow-out pond during culture for spawning event 3. Dashed vertical lines indicate sample points T1, T2, and T3. Dissolved oxygen and temperature are measures three times a day, in the morning (blue), afternoon (red), and evening (green).

Spawning event 3 has similarly low levels of salinity compared to spawning event 2. This pond was stocked about a week after the pond used for spawning event 2, so it experiences the same steep decline in temperature follow by a gradualt increase but then experiences a second similarly steep but even more drastic drop in temperatures after which the temperatures remain low.

Fig 3: Correlation among physical parameters (temperature, dissolved oxygen, pH, and salinity) measured in each grow-out pond (example spawning event 1).

Morning, evening, and afternoon measurements of temperature are correlated. The same pattern is observed for dissolved oxygen.

Fig 4: Comparison of distribution of physical parameters in grow-out ponds of spawning events 1 (blue), 2 (green), and 3 (red)).

Not all sampled progeny experienced the entire range of values, i.e. they are removed at different time points. Calculate mean values for three time ranges (day progeny are stocked to time points 1 - 3).

Fig 5: Comparison of distribution of physical parameters in grow-out ponds of spawning events 1 (blue), 2 (green), and 3 (red)).

Test for significant differences among physical parameters of grow-out ponds for each time range per spawning event.

Temperature (morning)

## 
##  RESULTS ANOVA

##              Df Sum Sq Mean Sq F value             Pr(>F)    
## RANGE         8   1562  195.29   12.09 0.0000000000000185 ***
## Residuals   237   3829   16.16                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2 observations deleted due to missingness